DO YOU KNOW?

 

# [x] + [x + 1/n ] + [x + 2/n ] + [x + 3/n ] + ----- + [x + (n-1)/n ] = [nx]   { [.] is G.I.F }

For example:- [x] + [x + 1/4] + [x + 2/4 ] + [x + 3/4 ] = [4x]

Question based on this formula:-

[x] + [x + 1/3] + [x + 2/3 ] = 6   ; Find the interval of x.

Sol. [x] + [x + 1/3 ] + [x + 2/3] = [3x] = 6 (given)

[3x] = 6

Therefore,  3x belongs to [6 , 7) .

Hence, x belongs to [2 , 7/3 ) .